Traditional statistical tools based on parametric models (e.g. p-values, ANOVA) for VI inference are dissatisfying due to restrictive assumptions often violated in modern datasets. Non-parametric extensions thus have been explored [1]}. In recent decades, many VI methods designed for modern deep learning models have been investigated; most of these methods are gradient-based and depend on the structure and the weights of nodes in a given specific neural network [2]}, [3]}, [4]}, [5]}. Few statistically rigorous properties are provided for these methods, and the VI definition is always intimately attached to the network itself, making it hard to interpret in a model-agnostic setting.
